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- W2952598112 abstract "The packing chromatic number $chi_{rho}(G)$ of a graph $G$ is the smallest integer $k$ such that there exists a $k$-vertex coloring of $G$ in which any two vertices receiving color $i$ are at distance at least $i+1$. It is proved that in the class of subcubic graphs the packing chromatic number is bigger than $13$, thus answering an open problem from [Gastineau, Togni, $S$-packing colorings of cubic graphs, Discrete Math. 339 (2016) 2461--2470]. In addition, the packing chromatic number is investigated with respect to several local operations. In particular, if $S_e(G)$ is the graph obtained from a graph $G$ by subdividing its edge $e$, then $leftlfloor chi_{rho}(G)/2 rightrfloor +1 le chi_{rho}(S_e(G)) le chi_{rho}(G)+1$." @default.
- W2952598112 created "2019-06-27" @default.
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- W2952598112 date "2016-08-19" @default.
- W2952598112 modified "2023-09-27" @default.
- W2952598112 title "Packing chromatic number under local changes in a graph" @default.
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